Each individual in a biological population is assumed to give birth at an exponential rate lambda, and to die at an exponential rate mu. In addition, there is an exponential rate of increase theta due to immigration. However, immigration is not allowed when the population is size N or larger.

a) set this up as a birth and death model

b) If N = 3, theta = lambda = 1, mu = 2, determine the proportion of time that immigration is restricted.

Any help is appreciated. Thanks